Using the results of Exercise 13.22, solve the problem of a thick-walled spherical shell with inner radius R₁ loaded with uniform pressure p₁, and with outer radius R₂ loaded with uniform pressure p₂. For the special case with p₁ = p and p₂ = 0, show that the stresses are given by:

Data from exercise 13.22

Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for the spherically symmetric case, where u_R = u(R), u_∅ = u_θ = 0. In particular, show that the governing equilibrium equation with zero body forces becomes:

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OR pR R-R 0 = 08 3 (-1 R pR (1 + R-R 2R